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Two blocks having masses 8kg and 16kg ar...

Two blocks having masses `8kg` and `16kg` are connected to the two ends of a light spring. The system is placed on a smooth horizontal floor. An inextensible string also connects B with ceiling as shown in the figure at the initial moment. Initially the spring has its natural length. A constant horizontal force F is applied to the heavier block as shown. What is the maximum possible value of F so the lighter block doesn't loose contact with ground?

Text Solution

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Draw `FBD` of `B` to get extension in spring. When block `B` just looses contact with ground resultant force on it is zero.

`Kx - T cos theta = 0 rArr T = (Kx)/(cos theta) , T sin theta + N - mg = 0`
When `N = 0` then `T sin theta = mg rArr (Kx)/(cos theta) sin theta = mg`
`x = (mg)/(K tan theta) = (80)/(K xx (4//3)) = (60)/(K)`
If spring has to just to just extend till this value then form work energy theorem we get
`Fx = (1)/(2) Kx^(2) rArr F = 30 N`.
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